FREE FIELD APPROACH TO D-BRANES IN N=2 SUPERCONFORMAL MINIMAL MODELS

2004 ◽  
Vol 19 (supp02) ◽  
pp. 294-310
Author(s):  
S. E. PARKHOMENKO
Keyword(s):  
Free Field ◽  
Virasoro Algebra ◽  
Minimal Models ◽  
Field Approach ◽  
Free Field Realization

The approach to construction of D-branes in the N=2 superconformal minimal models based on a free-field realization of the N=2 super-Virasoro algebra unitary modules is represented.

scholarly journals The N = 1 super Heisenberg–Virasoro vertex algebra at level zero

2021 ◽  
Author(s):  
Dražen Adamović ◽  
Berislav Jandrić ◽  
Gordan Radobolja
Keyword(s):  
Fock Space ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Algebra ◽  
Verma Modules ◽  
Minimal Models ◽  
Highest Weight ◽  
Level Zero ◽  
Free Field Realization ◽  
Highest Weight Representations

We study the representation theory of the [Formula: see text] super Heisenberg–Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg–Virasoro vertex algebra [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra 219(10) (2015) 4322–4342; D. Adamović and G. Radobolja, Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero, Commun. Contemp. Math. 21(2) (2019) 1850008; Y. Billig, Representations of the twisted Heisenberg–Virasoro algebra at level zero, Can. Math. Bull. 46(4) (2003) 529–537] to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras [D. Adamović and A. Milas, On W-algebras associated to [Formula: see text] minimal models and their representations, Int. Math. Res. Notices 2010(20) (2010) 3896–3934].

scholarly journals Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications

2015 ◽  
Vol 219 (10) ◽  
pp. 4322-4342 ◽  
Author(s):  
Dražen Adamović ◽  
Gordan Radobolja
Keyword(s):  
Free Field ◽  
Virasoro Algebra ◽  
Level Zero ◽  
Free Field Realization

PHYSICAL PROPERTIES OF W GRAVITIES AND W STRINGS

1991 ◽  
Vol 06 (33) ◽  
pp. 3055-3069 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
S. KALYANA RAMA
Keyword(s):  
Free Energy ◽  
Physical Properties ◽  
Configuration Space ◽  
Extra Dimension ◽  
Free Field ◽  
Two Dimensional ◽  
Minimal Models ◽  
Critical Dimensions ◽  
Free Field Realization ◽  
Dimensional Gravity

We investigate some basic physical properties of W gravities and W strings, using a free field realization. We argue that the configuration space of W gravities have global characteristics in addition to the Euler characteristic. We identify one such global quantity to be a "monopole" charge and show how this charge appears in the exponents. The free energy would then involve a "θ" parameter. Using a BRST procedure we find all the physical states of W3 and W4 gravities, and show that physical operators are nonsingular composites of the screening charge operators. (The latter are not physical operators for N≥3.) For W strings we show how the W constraints lead to the emergence of a single (and not many) extra dimension coming from the W-gravity sector. By analyzing the resulting dispersion relations we find that both the lower and upper critical dimensions are lowered compared to ordinary two-dimensional gravity. The pure W gravity spectrum reveals an intriguing "numerological" connection with unitary minimal models coupled to ordinary gravity.

scholarly journals Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero

2019 ◽  
Vol 21 (02) ◽  
pp. 1850008 ◽  
Author(s):  
Dražen Adamović ◽  
Gordan Radobolja
Keyword(s):  
Free Field ◽  
Virasoro Algebra ◽  
Large Family ◽  
Verma Modules ◽  
Irreducible Modules ◽  
Level Zero ◽  
Free Field Realization ◽  
Dual Module ◽  
Whittaker Modules ◽  
New Applications

This paper is a continuation of [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra 219(10) (2015) 4322–4342]. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg–Virasoro algebra [Formula: see text] at level zero. We find explicit formulas for singular vectors in certain Verma modules. A free field realization of self-dual modules for [Formula: see text] is presented by combining a bosonic construction of Whittaker modules from [D. Adamović, R. Lu and K. Zhao, Whittaker modules for the affine Lie algebra [Formula: see text], Adv. Math. 289 (2016) 438–479; arXiv:1409.5354] with a construction of logarithmic modules for vertex algebras. As an application, we prove that there exists a non-split self-extension of irreducible self-dual module which is a logarithmic module of rank two. We construct a large family of logarithmic modules containing different types of highest weight modules as subquotients. We believe that these logarithmic modules are related with projective covers of irreducible modules in a suitable category of [Formula: see text]-modules.

scholarly journals BOSONIZATION OF A TOPOLOGICAL COSET MODEL AND NON-CRITICAL STRING THEORY

1994 ◽  
Vol 09 (06) ◽  
pp. 541-547 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
String Theory ◽  
Free Field ◽  
Superconformal Algebra ◽  
Minimal Models ◽  
Total Derivative ◽  
Coset Model ◽  
Free Field Realization ◽  
Topological Field ◽  
The Subject ◽  
Coset Models

We analyze the relation between a topological coset model based on super SL(2, R)/U(1) coset and non-critical string theory by using free field realization. We show that the twisted N=2 algebra of the coset model can be naturally transformed into that of non-critical string. The screening operators of the coset models can be identified either with those of the minimal matters or with the cosmological constant operator. We also find that another screening operator, which is intrinsic in our approach, becomes the BRST non-trivial state of ghost number 0 (generator of the ground ring for c=1 gravity). The relation between non-critical strings and topological field theories is the subject of current interest. It has long been suggested that the latter theories describe the unbroken phase of gravity,1 but their precise relation has not been clear. It has been known that the twisting of N=2 superconformal field theory gives rise to topological theory.1,2 This suggests that any non-critical string theories may have hidden N=2 superconformal symmetry. Indeed, several authors have observed that the BRST current and the antighost field b(z) generate an algebra that is quite similar but apparently not identical to the N=2 superconformal algebra.3 It turns out that the BRST current can be modified by total derivative terms so that the antighost and the physical BRST current exactly generate a topologically twisted N=2 superconformal algebra.4,5 This does not identify, however, the structure of the models with N=2 symmetry. Recently, rather non-trivial correspondence between super SL(2, R)k/U(1) coset model6 and c=1 string has been analyzed through twisted N=2 structure. Mukhi and Vafa7 have revealed an amazing correspondence between these two models for k=3. In this letter, we discuss the relation of these models and the generalization of the correspondence to the minimal models coupled to gravity by means of the free field realization. We find that there is another interesting correspondence for k=1. Super SL(2, R)k/U(1) model is described by the bosonic coset model of SL(2, R)k×U(1)/U(1).8 For a representation of SL(2, R)k, we use the following

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

SPECTRAL FLOW AND FREE FIELD REALIZATIONS OF BOSONIC STRINGS ON NAPPI–WITTEN GROUP MANIFOLD

2011 ◽  
Vol 26 (01) ◽  
pp. 149-160
Author(s):  
GANG CHEN
Keyword(s):  
Lie Algebra ◽  
Bosonic Strings ◽  
Free Field ◽  
Geometric Interpretation ◽  
Closed String ◽  
Space Time ◽  
Spectral Flow ◽  
Affine Lie Algebra ◽  
Group Manifold ◽  
Free Field Realization

In this paper we study some aspects of closed string theories in the Nappi–Witten space–time. The effects of spectral flow on the geodesics are studied in terms of an explicit parametrization of the group manifold. The worldsheets of the closed strings under the spectral flow of the geodesics can be classified into four classes, each with a geometric interpretation. We also obtain a free field realization of the Nappi–Witten affine Lie algebra in the most general conditions using a different but equivalent parametrization of the group manifold.

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

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